Search results for: Tracking algorithm.

Authors: Drahoslava Janovska, Vladimir Janovsky, Kunio Tanabe

Abstract:

A proof of convergence of a new continuation algorithm for computing the Analytic SVD for a large sparse parameter– dependent matrix is given. The algorithm itself was developed and numerically tested in [5].

Keywords: Analytic Singular Value Decomposition, large sparse parameter–dependent matrices, continuation algorithm of a predictorcorrector type.

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Authors: Yen San Yong, Hock Woon Hon

Abstract:

An algorithm for estimating the disparity of objects of interest is proposed. This algorithm uses image shifting and overlapping area to estimate the disparity value; thereby depth of the objects of interest can be obtained. The algorithm is able to perform at different levels of accuracy. However, as the accuracy increases the processing speed decreases. The algorithm is tested with static stereo images and sequence of stereo images. The experimental results are presented in this paper.

Keywords: stereo vision, binocular parallax

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Authors: Chau Nguyen Viet, Ian Marshall

Abstract:

This paper presents a new classification algorithm using colour and texture for obstacle detection. Colour information is computationally cheap to learn and process. However in many cases, colour alone does not provide enough information for classification. Texture information can improve classification performance but usually comes at an expensive cost. Our algorithm uses both colour and texture features but texture is only needed when colour is unreliable. During the training stage, texture features are learned specifically to improve the performance of a colour classifier. The algorithm learns a set of simple texture features and only the most effective features are used in the classification stage. Therefore our algorithm has a very good classification rate while is still fast enough to run on a limited computer platform. The proposed algorithm was tested with a challenging outdoor image set. Test result shows the algorithm achieves a much better trade-off between classification performance and efficiency than a typical colour classifier.

Keywords: Colour, texture, classification, obstacle detection.

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Authors: Essam Al Daoud

Abstract:

Genome rearrangement is an important area in computational biology and bioinformatics. The basic problem in genome rearrangements is to compute the edit distance, i.e., the minimum number of operations needed to transform one genome into another. Unfortunately, unsigned genome rearrangement problem is NP-hard. In this study an improved ant colony optimization algorithm to approximate the edit distance is proposed. The main idea is to convert the unsigned permutation to signed permutation and evaluate the ants by using Kaplan algorithm. Two new operations are added to the standard ant colony algorithm: Replacing the worst ants by re-sampling the ants from a new probability distribution and applying the crossover operations on the best ants. The proposed algorithm is tested and compared with the improved breakpoint reversal sort algorithm by using three datasets. The results indicate that the proposed algorithm achieves better accuracy ratio than the previous methods.

Keywords: Ant colony algorithm, Edit distance, Genome breakpoint, Genome rearrangement, Reversal sort.

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Authors: K. B. Cullen, G. C. M. Silvestre, N. J. Hurley

Abstract:

This paper presents software tools that convert the C/Cµ floating point source code for a DSP algorithm into a fixedpoint simulation model that can be used to evaluate the numericalperformance of the algorithm on several different fixed pointplatforms including microprocessors, DSPs and FPGAs. The tools use a novel system for maintaining binary point informationso that the conversion from floating point to fixed point isautomated and the resulting fixed point algorithm achieves maximum possible precision. A configurable architecture is used during the simulation phase so that the algorithm can produce a bit-exact output for several different target devices.

Keywords: DSP devices, DSP algorithm, simulation model, software

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Authors: R. Rajabpour, N. Talebbeydokhti, M. H. Ahmadi

Abstract:

In recent years, new techniques for solving complex problems in engineering are proposed. One of these techniques is JPSO algorithm. With innovative changes in the nature of the jump algorithm JPSO, it is possible to construct a graph-based solution with a new algorithm called G-JPSO. In this paper, a new algorithm to solve the optimal control problem Fletcher-Powell and optimal control of pumps in water distribution network was evaluated. Optimal control of pumps comprise of optimum timetable operation (status on and off) for each of the pumps at the desired time interval. Maximum number of status on and off for each pumps imposed to the objective function as another constraint. To determine the optimal operation of pumps, a model-based optimization-simulation algorithm was developed based on G-JPSO and JPSO algorithms. The proposed algorithm results were compared well with the ant colony algorithm, genetic and JPSO results. This shows the robustness of proposed algorithm in finding near optimum solutions with reasonable computational cost.

Keywords: G-JPSO, operation, optimization, pumping station, water distribution networks.

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Authors: J.-C. Cexus, A.O. Boudraa

Abstract:

In this paper, a new approach for target recognition based on the Empirical mode decomposition (EMD) algorithm of Huang etal. [11] and the energy tracking operator of Teager [13]-[14] is introduced. The conjunction of these two methods is called Teager-Huang analysis. This approach is well suited for nonstationary signals analysis. The impulse response (IR) of target is first band pass filtered into subsignals (components) called Intrinsic mode functions (IMFs) with well defined Instantaneous frequency (IF) and Instantaneous amplitude (IA). Each IMF is a zero-mean AM-FM component. In second step, the energy of each IMF is tracked using the Teager energy operator (TEO). IF and IA, useful to describe the time-varying characteristics of the signal, are estimated using the Energy separation algorithm (ESA) algorithm of Maragos et al .[16]-[17]. In third step, a set of features such as skewness and kurtosis are extracted from the IF, IA and IMF energy functions. The Teager-Huang analysis is tested on set of synthetic IRs of Sonar targets with different physical characteristics (density, velocity, shape,? ). PCA is first applied to features to discriminate between manufactured and natural targets. The manufactured patterns are classified into spheres and cylinders. One hundred percent of correct recognition is achieved with twenty three echoes where sixteen IRs, used for training, are free noise and seven IRs, used for testing phase, are corrupted with white Gaussian noise.

Keywords: Target recognition, Empirical mode decomposition, Teager-Kaiser energy operator, Features extraction.

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Authors: Aleksandar Tsenov

Abstract:

The main goal of this work is to propose a way for combined use of two nontraditional algorithms by solving topological problems on telecommunications concentrator networks. The algorithms suggested are the Simulated Annealing algorithm and the Genetic Algorithm. The Algorithm of Simulated Annealing unifies the well known local search algorithms. In addition - Simulated Annealing allows acceptation of moves in the search space witch lead to decisions with higher cost in order to attempt to overcome any local minima obtained. The Genetic Algorithm is a heuristic approach witch is being used in wide areas of optimization works. In the last years this approach is also widely implemented in Telecommunications Networks Planning. In order to solve less or more complex planning problem it is important to find the most appropriate parameters for initializing the function of the algorithm.

Keywords: Concentrator network, genetic algorithm, simulated annealing, UCPL.

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Authors: Hoshang Kolivand, Mahyar Kolivand, Mohd Shahrizal Sunar, Mohd Azhar M. Arsad

Abstract:

Real-time shadow generation in virtual environments and Augmented Reality (AR) was always a hot topic in the last three decades. Lots of calculation for shadow generation among AR needs a fast algorithm to overcome this issue and to be capable of implementing in any real-time rendering. In this paper, a silhouette detection algorithm is presented to generate shadows for AR systems. Δ+ algorithm is presented based on extending edges of occluders to recognize which edges are silhouettes in the case of real-time rendering. An accurate comparison between the proposed algorithm and current algorithms in silhouette detection is done to show the reduction calculation by presented algorithm. The algorithm is tested in both virtual environments and AR systems. We think that this algorithm has the potential to be a fundamental algorithm for shadow generation in all complex environments.

Keywords: Silhouette detection, shadow volumes, real-time shadows, rendering, augmented reality.

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Authors: Mohammed M. Siddeq, Mohammed H. Rasheed, Omar M. Salih, Marcos A. Rodrigues

Abstract:

This research proposes a data encoding and decoding method based on the Matrix Minimization algorithm. This algorithm is applied to high-frequency coefficients for compression/encoding. The algorithm starts by converting every three coefficients to a single value; this is accomplished based on three different keys. The decoding/decompression uses a search method called QSS (Quick Sequential Search) Decoding Algorithm presented in this research based on the sequential search to recover the exact coefficients. In the next step, the decoded data are saved in an auxiliary array. The basic idea behind the auxiliary array is to save all possible decoded coefficients; this is because another algorithm, such as conventional sequential search, could retrieve encoded/compressed data independently from the proposed algorithm. The experimental results showed that our proposed decoding algorithm retrieves original data faster than conventional sequential search algorithms.

Keywords: Matrix Minimization Algorithm, Decoding Sequential Search Algorithm, image compression, Discrete Cosine Transform, Discrete Wavelet Transform.

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Authors: M. Taha, Hala H. Zayed, T. Nazmy, M. Khalifa

Abstract:

Recently, traffic monitoring has attracted the attention of computer vision researchers. Many algorithms have been developed to detect and track moving vehicles. In fact, vehicle tracking in daytime and in nighttime cannot be approached with the same techniques, due to the extreme different illumination conditions. Consequently, traffic-monitoring systems are in need of having a component to differentiate between daytime and nighttime scenes. In this paper, a HSV-based day/night detector is proposed for traffic monitoring scenes. The detector employs the hue-histogram and the value-histogram on the top half of the image frame. Experimental results show that the extraction of the brightness features along with the color features within the top region of the image is effective for classifying traffic scenes. In addition, the detector achieves high precision and recall rates along with it is feasible for real time applications.

Keywords: Day/night detector, daytime/nighttime classification, image classification, vehicle tracking, traffic monitoring.

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Authors: Wen-Tzu Chen, Wen-Bin Kao

Abstract:

This paper provides a scheme to improve the read efficiency of anti-collision algorithm in EPCglobal UHF Class-1 Generation-2 RFID standard. In this standard, dynamic frame slotted ALOHA is specified to solve the anti-collision problem. Also, the Q-algorithm with a key parameter C is adopted to dynamically adjust the frame sizes. In the paper, we split the C parameter into two parameters to increase the read speed and derive the optimal values of the two parameters through simulations. The results indicate our method outperforms the original Q-algorithm.

Keywords: RFID, anti-collision, Q algorithm, ALOHA

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Authors: Mustafa Kisa, Fatih Mehmet Botsali

Abstract:

Recent developments in automotive technology are focused on economy, comfort and safety. Vehicle tracking and collision detection systems are attracting attention of many investigators focused on safety of driving in the field of automotive mechatronics. In this paper, a vision-based vehicle detection system is presented. Developed system is intended to be used in collision detection and driver alert. The system uses RGB images captured by a camera in a car driven in the highway. Images captured by the moving camera are used to detect the moving vehicles in the image. A vehicle ahead of the camera is detected in daylight conditions. The proposed method detects moving vehicles by subtracting successive images. Plate height of the vehicle is determined by using a plate recognition algorithm. Distance of the moving object is calculated by using the plate height. After determination of the distance of the moving vehicle relative speed of the vehicle and Time-to-Collision are calculated by using distances measured in successive images. Results obtained in road tests are discussed in order to validate the use of the proposed method.

Keywords: Image possessing, vehicle tracking, license plate detection, computer vision.

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Authors: Zaineb Ben Messaoud, Dorra Gargouri, Saida Zribi, Ahmed Ben Hamida

Abstract:

This paper presents a formant-tracking linear prediction (FTLP) model for speech processing in noise. The main focus of this work is the detection of formant trajectory based on Hidden Markov Models (HMM), for improved formant estimation in noise. The approach proposed in this paper provides a systematic framework for modelling and utilization of a time- sequence of peaks which satisfies continuity constraints on parameter; the within peaks are modelled by the LP parameters. The formant tracking LP model estimation is composed of three stages: (1) a pre-cleaning multi-band spectral subtraction stage to reduce the effect of residue noise on formants (2) estimation stage where an initial estimate of the LP model of speech for each frame is obtained (3) a formant classification using probability models of formants and Viterbi-decoders. The evaluation results for the estimation of the formant tracking LP model tested in Gaussian white noise background, demonstrate that the proposed combination of the initial noise reduction stage with formant tracking and LPC variable order analysis, results in a significant reduction in errors and distortions. The performance was evaluated with noisy natual vowels extracted from international french and English vocabulary speech signals at SNR value of 10dB. In each case, the estimated formants are compared to reference formants.

Keywords: Formants Estimation, HMM, Multi Band Spectral Subtraction, Variable order LPC coding, White Gauusien Noise.

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Authors: Soottipoom Yaowiwat, Manoj Lohatepanont, Proadpran Punyabukkana

Abstract:

Several approaches such as linear programming, network modeling, greedy heuristic and decision support system are well-known approaches in solving irregular airline operation problem. This paper presents an alternative approach based on Multi Objective Micro Genetic Algorithm. The aim of this research is to introduce the concept of Multi Objective Micro Genetic Algorithm as a tool to solve irregular airline operation, combine and reroute problem. The experiment result indicated that the model could obtain optimal solutions within a few second.

Keywords: Irregular Airline Operation, Combine and RerouteRoutine, Genetic Algorithm, Micro Genetic Algorithm, Multi ObjectiveOptimization, Evolutionary Algorithm.

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Authors: Radhwan Yousif Sedik Al-Jawadi

Abstract:

Optimization is necessary for finding appropriate solutions to a range of real-life problems. In particular, genetic (or more generally, evolutionary) algorithms have proved very useful in solving many problems for which analytical solutions are not available. In this paper, we present an optimization algorithm called Dynamic Schema with Dissimilarity and Similarity of Chromosomes (DSDSC) which is a variant of the classical genetic algorithm. This approach constructs new chromosomes from a schema and pairs of existing ones by exploring their dissimilarities and similarities. To show the effectiveness of the algorithm, it is tested and compared with the classical GA, on 15 two-dimensional optimization problems taken from literature. We have found that, in most cases, our method is better than the classical genetic algorithm.

Keywords: Genetic algorithm, similarity and dissimilarity, chromosome injection, dynamic schema.

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Authors: H. H. Huynh, J. Meunier, J.Sequeira, M.Daniel

Abstract:

In this paper, the detection and tracking of face, mouth, hands and medication bottles in the context of medication intake monitoring with a camera is presented. This is aimed at recognizing medication intake for elderly in their home setting to avoid an inappropriate use. Background subtraction is used to isolate moving objects, and then, skin and bottle segmentations are done in the RGB normalized color space. We use a minimum displacement distance criterion to track skin color regions and the R/G ratio to detect the mouth. The color-labeled medication bottles are simply tracked based on the color space distance to their mean color vector. For the recognition of medication intake, we propose a three-level hierarchal approach, which uses activity-patterns to recognize the normal medication intake activity. The proposed method was tested with three persons, with different medication intake scenarios, and gave an overall precision of over 98%.

Keywords: Activity recognition, background subtraction, tracking, medication intake, video surveillance

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Authors: Cesar Hernández, Diego Giral, Ingrid Páez

Abstract:

This article proposes a hybrid algorithm for spectrum allocation in cognitive radio networks based on the algorithms Analytical Hierarchical Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to improve the performance of the spectrum mobility of secondary users in cognitive radio networks. To calculate the level of performance of the proposed algorithm a comparative analysis between the proposed AHP-TOPSIS, Grey Relational Analysis (GRA) and Multiplicative Exponent Weighting (MEW) algorithm is performed. Four evaluation metrics are used. These metrics are accumulative average of failed handoffs, accumulative average of handoffs performed, accumulative average of transmission bandwidth, and accumulative average of the transmission delay. The results of the comparison show that AHP-TOPSIS Algorithm provides 2.4 times better performance compared to a GRA Algorithm and, 1.5 times better than the MEW Algorithm.

Keywords: Cognitive radio, decision making, hybrid algorithm, spectrum handoff, wireless networks.

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Authors: Meng Wang, Qi-rui Han

Abstract:

Because of excellent properties, people has paid more attention to SPIHI algorithm, which is based on the traditional wavelet transformation theory, but it also has its shortcomings. Combined the progress in the present wavelet domain and the human's visual characteristics, we propose an improved algorithm based on human visual characteristics of SPIHT in the base of analysis of SPIHI algorithm. The experiment indicated that the coding speed and quality has been enhanced well compared to the original SPIHT algorithm, moreover improved the quality of the transmission cut off.

Keywords: Lifted wavelet transform, SPIHT, Human Visual Characteristics.

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Authors: Chang Liu, Zishu He

Abstract:

Adaptive echo cancellers with two-path algorithm are applied to avoid the false adaptation during the double-talk situation. In the two-path algorithm, several transfer logic solutions have been proposed to control the filter update. This paper presents an improved transfer logic solution. It improves the convergence speed of the two-path algorithm, and allows the reduction of the memory elements and computational complexity. Results of simulations show the improved performance of the proposed solution.

Keywords: Acoustic echo cancellation, Echo return lossenhancement (ERLE), Two-path algorithm, Transfer logic

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Authors: Awadhesh Kumar Singh

Abstract:

Jayanti-s algorithm is one of the best known abortable mutual exclusion algorithms. This work is an attempt to overcome an already known limitation of the algorithm while preserving its all important properties and elegance. The limitation is that the token number used to assign process identification number to new incoming processes is unbounded. We have used a suitably adapted alternative data structure, in order to completely eliminate the use of token number, in the algorithm.

Keywords: Abortable, deterministic, local spin, mutual exclusion.

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Authors: R.Mostafaei, A.Habiboghli, M.R.Meybodi

Abstract:

In distributed resource allocation a set of agents must assign their resources to a set of tasks. This problem arises in many real-world domains such as distributed sensor networks, disaster rescue, hospital scheduling and others. Despite the variety of approaches proposed for distributed resource allocation, a systematic formalization of the problem, explaining the different sources of difficulties, and a formal explanation of the strengths and limitations of key approaches is missing. We take a step towards this goal by using a formalization of distributed resource allocation that represents both dynamic and distributed aspects of the problem. In this paper we present a new idea for target tracking in sensor networks and compare it with previous approaches. The central contribution of the paper is a generalized mapping from distributed resource allocation to DDCSP. This mapping is proven to correctly perform resource allocation problems of specific difficulty. This theoretical result is verified in practice by a simulation on a realworld distributed sensor network.

Keywords: Distributed CSP, Target Tracking, Sensor Network

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: Mourad Ykhlef, Hebah ElGibreen

Abstract:

Mining Sequential Patterns in large databases has become an important data mining task with broad applications. It is an important task in data mining field, which describes potential sequenced relationships among items in a database. There are many different algorithms introduced for this task. Conventional algorithms can find the exact optimal Sequential Pattern rule but it takes a long time, particularly when they are applied on large databases. Nowadays, some evolutionary algorithms, such as Particle Swarm Optimization and Genetic Algorithm, were proposed and have been applied to solve this problem. This paper will introduce a new kind of hybrid evolutionary algorithm that combines Genetic Algorithm (GA) with Particle Swarm Optimization (PSO) to mine Sequential Pattern, in order to improve the speed of evolutionary algorithms convergence. This algorithm is referred to as SP-GAPSO.

Keywords: Genetic Algorithm, Hybrid Evolutionary Algorithm, Particle Swarm Optimization algorithm, Sequential Pattern mining.

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Authors: Qin Ding, Jim Gasvoda

Abstract:

Clustering is the process of subdividing an input data set into a desired number of subgroups so that members of the same subgroup are similar and members of different subgroups have diverse properties. Many heuristic algorithms have been applied to the clustering problem, which is known to be NP Hard. Genetic algorithms have been used in a wide variety of fields to perform clustering, however, the technique normally has a long running time in terms of input set size. This paper proposes an efficient genetic algorithm for clustering on very large data sets, especially on image data sets. The genetic algorithm uses the most time efficient techniques along with preprocessing of the input data set. We test our algorithm on both artificial and real image data sets, both of which are of large size. The experimental results show that our algorithm outperforms the k-means algorithm in terms of running time as well as the quality of the clustering.

Keywords: Clustering, data mining, genetic algorithm, image data.

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Authors: Jeffrey L. Duffany

Abstract:

An optimal solution for a large number of constraint satisfaction problems can be found using the technique of substitution and elimination of variables analogous to the technique that is used to solve systems of equations. A decision function f(A)=max(A2) is used to determine which variables to eliminate. The algorithm can be expressed in six lines and is remarkable in both its simplicity and its ability to find an optimal solution. However it is inefficient in that it needs to square the updated A matrix after each variable elimination. To overcome this inefficiency the algorithm is analyzed and it is shown that the A matrix only needs to be squared once at the first step of the algorithm and then incrementally updated for subsequent steps, resulting in significant improvement and an algorithm complexity of O(n3).

Keywords: Algorithm, complexity, constraint, np-complete.

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Authors: Adrià Arbués-Sangüesa, Coloma Ballester, Gloria Haro

Abstract:

Tracking sports players is a widely challenging scenario, specially in single-feed videos recorded in tight courts, where cluttering and occlusions cannot be avoided. This paper presents an analysis of several geometric and semantic visual features to detect and track basketball players. An ablation study is carried out and then used to remark that a robust tracker can be built with Deep Learning features, without the need of extracting contextual ones, such as proximity or color similarity, nor applying camera stabilization techniques. The presented tracker consists of: (1) a detection step, which uses a pretrained deep learning model to estimate the players pose, followed by (2) a tracking step, which leverages pose and semantic information from the output of a convolutional layer in a VGG network. Its performance is analyzed in terms of MOTA over a basketball dataset with more than 10k instances.

Keywords: Basketball, deep learning, feature extraction, single-camera, tracking.

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Authors: Abdel-Reza Hatamlou, Mohammad Reza Meybodi

Abstract:

In this paper we present a hybrid search algorithm for solving constraint satisfaction and optimization problems. This algorithm combines ideas of two basic approaches: complete and incomplete algorithms which also known as systematic search and local search algorithms. Different characteristics of systematic search and local search methods are complementary. Therefore we have tried to get the advantages of both approaches in the presented algorithm. The major advantage of presented algorithm is finding partial sound solution for complicated problems which their complete solution could not be found in a reasonable time. This algorithm results are compared with other algorithms using the well known n-queens problem.

Keywords: Constraint Satisfaction Problem, Hybrid SearchAlgorithm.

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Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

This paper presents a prediction performance of feedforward Multilayer Perceptron (MLP) and Echo State Networks (ESN) trained with extended Kalman filter. Feedforward neural networks and ESN are powerful neural networks which can track and predict nonlinear signals. However, their tracking performance depends on the specific signals or data sets, having the risk of instability accompanied by large error. In this study we explore this process by applying different network size and leaking rate for prediction of nonlinear or chaotic signals in MLP neural networks. Major problems of ESN training such as the problem of initialization of the network and improvement in the prediction performance are tackled. The influence of coefficient of activation function in the hidden layer and other key parameters are investigated by simulation results. Extended Kalman filter is employed in order to improve the sequential and regulation learning rate of the feedforward neural networks. This training approach has vital features in the training of the network when signals have chaotic or non-stationary sequential pattern. Minimization of the variance in each step of the computation and hence smoothing of tracking were obtained by examining the results, indicating satisfactory tracking characteristics for certain conditions. In addition, simulation results confirmed satisfactory performance of both of the two neural networks with modified parameterization in tracking of the nonlinear signals.

Keywords: Feedforward neural networks, nonlinear signal prediction, echo state neural networks approach, leaking rates, capacity of neural networks.

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Authors: Li Ni, Pen ManMan, Li KenLi

Abstract:

Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, research has investigated the utility of evolutionary computing and related techniques in the regard. Chemical Reaction Optimization (CRO) is a recently established method. So the property embedded in CRO is used to solve optimization problems. This paper presents an algorithm framework (EM-CRO) with modified CRO operators based on EM cluster problems. The hybrid algorithm is mainly to solve the problem of initial value sensitivity of the objective function optimization clustering algorithm. Our experiments mainly take the EM classic algorithm:k-means and fuzzy k-means as an example, through the CRO algorithm to optimize its initial value, get K-means-CRO and FKM-CRO algorithm. The experimental results of them show that there is improved efficiency for solving objective function optimization clustering problems.

Keywords: Chemical reaction optimization, expectation maximization, initial, objective function clustering.

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